Which of the following can be used to prove triangle similarity, but not congruence? Circle your answer. Is it SSS, AAA, ASA, or RHS?
Let’s begin by recapping what we actually mean by similarity and what we mean by congruence. When two shapes are similar, they are enlargements of one another. For this reason, they must have three angles the same size, but the lengths of their sides will be different.
Congruent shapes however are identical. They will have exactly the same angles and the exact same length sides in the same order. For this reason, SSS, side side side can be used to prove congruency, as can SAS, side angle side; ASA, angle side angle; and RHS, that’s a right angle, a hypotenuse, and one other side.
We can see that we can therefore discount SSS, ASA, and RHS in our list. And we’re left with AAA, angle angle angle. We said that similar shapes are enlargements of one another and their angles are the same, so this makes sense. The condition that can be used to prove triangle similarity but not congruence is AAA.